What is the derivate of...?

Question

$sin (x y) + e^{x y} = e^{x}$ $sin(xy)+e^(xy)=e^x$

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Answer 1 · 2018-06-12T00:05:41

$y'= (e^x-y(cosx(xy)+e^(xy)))/(x(cosx(xy)+e^(xy)))$

Differentiate both sides of the equation:

$d/dx (sin(xy)+e^(xy)) = d/dx e^x$

$(y+xy')cosx(xy)+(y+xy')e^(xy) = e^x$

$y(cosx(xy)+e^(xy)) +xy'(cosx(xy)+e^(xy)) = e^x$

Solve now for $y'$ :

$y'= (e^x-y(cosx(xy)+e^(xy)))/(x(cosx(xy)+e^(xy)))$